Analytic pro-p groups:
The first edition of this book was the indispensable reference for researchers in the theory of pro-p groups. In this second edition the presentation has been improved and important new material has been added. The first part of the book is group-theoretic. It develops the theory of pro-p groups of...
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1999
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Cambridge studies in advanced mathematics
61 |
| Schlagworte: | |
| Online-Zugang: | DE-12 DE-92 DE-355 DE-706 Volltext |
| Zusammenfassung: | The first edition of this book was the indispensable reference for researchers in the theory of pro-p groups. In this second edition the presentation has been improved and important new material has been added. The first part of the book is group-theoretic. It develops the theory of pro-p groups of finite rank, starting from first principles and using elementary methods. Part II introduces p-adic analytic groups: by taking advantage of the theory developed in Part I, it is possible to define these, and derive all the main results of p-adic Lie theory, without having to develop any sophisticated analytic machinery. Part III, consisting of new material, takes the theory further. Among those topics discussed are the theory of pro-p groups of finite coclass, the dimension subgroup series, and its associated graded Lie algebra. The final chapter sketches a theory of analytic groups over pro-p rings other than the p-adic integers |
| Beschreibung: | 1 online resource (xviii, 368 Seiten) |
| ISBN: | 9780511470882 |
| DOI: | 10.1017/CBO9780511470882 |
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| 245 | 1 | 0 | |a Analytic pro-p groups |c J.D. Dixon, Carleton University, Ottawa, M.P.F. du Sautoy, University of Cambridge, A. Mann, Hebrew University, Jerusalem, D. Segal, All Souls College Oxford; Revised and enlarged by Marcus du Sautoy & Dan Segal |
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| 490 | 1 | |a Cambridge studies in advanced mathematics |v 61 | |
| 505 | 8 | |a Pt. I. Pro-p groups -- 1. Profinite groups and pro-p groups -- 2. Powerful p-groups -- 3. Pro-p groups of finite rank -- 4. Uniformly powerful groups -- 5. Automorphism groups -- Interlude A. 'Fascicule de resultats': pro-p groups of finite rank -- Pt. II. Analytic groups -- 6. Normed algebras -- 7. The group algebra -- Interlude B. Linearity criteria -- 8. p-adic analytic groups -- Interlude C. Finitely generated groups, p-adic analytic groups and Poincare series -- 9. Lie theory -- Pt. III. Further topics -- 10. Pro-p groups of finite coclass -- 11. Dimension subgroup methods -- 12. Some graded algebras -- Interlude D. The Golod-Shafarevich inequality -- Interlude E. Groups of sub-exponential growth -- 13. Analytic groups over pro-p rings -- App. A. The Hall-Petrescu formula -- App. B. Topological groups | |
| 520 | |a The first edition of this book was the indispensable reference for researchers in the theory of pro-p groups. In this second edition the presentation has been improved and important new material has been added. The first part of the book is group-theoretic. It develops the theory of pro-p groups of finite rank, starting from first principles and using elementary methods. Part II introduces p-adic analytic groups: by taking advantage of the theory developed in Part I, it is possible to define these, and derive all the main results of p-adic Lie theory, without having to develop any sophisticated analytic machinery. Part III, consisting of new material, takes the theory further. Among those topics discussed are the theory of pro-p groups of finite coclass, the dimension subgroup series, and its associated graded Lie algebra. The final chapter sketches a theory of analytic groups over pro-p rings other than the p-adic integers | ||
| 650 | 4 | |a Nilpotent groups | |
| 650 | 4 | |a p-adic groups | |
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Datensatz im Suchindex
| _version_ | 1805088027408596992 |
|---|---|
| adam_text | |
| any_adam_object | |
| author | Dixon, John D. 1937- Du Sautoy, Marcus 1965- Mann, Avinoam 1937- Segal, Daniel 1947- |
| author_GND | (DE-588)1031802444 (DE-588)122205731 (DE-588)173586686 (DE-588)133203670 |
| author_facet | Dixon, John D. 1937- Du Sautoy, Marcus 1965- Mann, Avinoam 1937- Segal, Daniel 1947- |
| author_role | aut aut aut aut |
| author_sort | Dixon, John D. 1937- |
| author_variant | j d d jd jdd s m d sm smd a m am d s ds |
| building | Verbundindex |
| bvnumber | BV043941275 |
| classification_rvk | SI 320 SK 260 SK 340 |
| collection | ZDB-20-CBO |
| contents | Pt. I. Pro-p groups -- 1. Profinite groups and pro-p groups -- 2. Powerful p-groups -- 3. Pro-p groups of finite rank -- 4. Uniformly powerful groups -- 5. Automorphism groups -- Interlude A. 'Fascicule de resultats': pro-p groups of finite rank -- Pt. II. Analytic groups -- 6. Normed algebras -- 7. The group algebra -- Interlude B. Linearity criteria -- 8. p-adic analytic groups -- Interlude C. Finitely generated groups, p-adic analytic groups and Poincare series -- 9. Lie theory -- Pt. III. Further topics -- 10. Pro-p groups of finite coclass -- 11. Dimension subgroup methods -- 12. Some graded algebras -- Interlude D. The Golod-Shafarevich inequality -- Interlude E. Groups of sub-exponential growth -- 13. Analytic groups over pro-p rings -- App. A. The Hall-Petrescu formula -- App. B. Topological groups |
| ctrlnum | (ZDB-20-CBO)CR9780511470882 (OCoLC)967679126 (DE-599)BVBBV043941275 |
| dewey-full | 512/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 |
| dewey-search | 512/.2 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511470882 |
| edition | Second edition |
| format | Electronic eBook |
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| id | DE-604.BV043941275 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T09:01:30Z |
| institution | BVB |
| isbn | 9780511470882 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350246 |
| oclc_num | 967679126 |
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| owner | DE-12 DE-92 DE-355 DE-BY-UBR DE-83 DE-706 |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR DE-83 DE-706 |
| physical | 1 online resource (xviii, 368 Seiten) |
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| publishDate | 1999 |
| publishDateSearch | 1999 |
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| publisher | Cambridge University Press |
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| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Dixon, John D. 1937- Verfasser (DE-588)1031802444 aut Analytic pro-p groups J.D. Dixon, Carleton University, Ottawa, M.P.F. du Sautoy, University of Cambridge, A. Mann, Hebrew University, Jerusalem, D. Segal, All Souls College Oxford; Revised and enlarged by Marcus du Sautoy & Dan Segal Second edition Cambridge Cambridge University Press 1999 1 online resource (xviii, 368 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 61 Pt. I. Pro-p groups -- 1. Profinite groups and pro-p groups -- 2. Powerful p-groups -- 3. Pro-p groups of finite rank -- 4. Uniformly powerful groups -- 5. Automorphism groups -- Interlude A. 'Fascicule de resultats': pro-p groups of finite rank -- Pt. II. Analytic groups -- 6. Normed algebras -- 7. The group algebra -- Interlude B. Linearity criteria -- 8. p-adic analytic groups -- Interlude C. Finitely generated groups, p-adic analytic groups and Poincare series -- 9. Lie theory -- Pt. III. Further topics -- 10. Pro-p groups of finite coclass -- 11. Dimension subgroup methods -- 12. Some graded algebras -- Interlude D. The Golod-Shafarevich inequality -- Interlude E. Groups of sub-exponential growth -- 13. Analytic groups over pro-p rings -- App. A. The Hall-Petrescu formula -- App. B. Topological groups The first edition of this book was the indispensable reference for researchers in the theory of pro-p groups. In this second edition the presentation has been improved and important new material has been added. The first part of the book is group-theoretic. It develops the theory of pro-p groups of finite rank, starting from first principles and using elementary methods. Part II introduces p-adic analytic groups: by taking advantage of the theory developed in Part I, it is possible to define these, and derive all the main results of p-adic Lie theory, without having to develop any sophisticated analytic machinery. Part III, consisting of new material, takes the theory further. Among those topics discussed are the theory of pro-p groups of finite coclass, the dimension subgroup series, and its associated graded Lie algebra. The final chapter sketches a theory of analytic groups over pro-p rings other than the p-adic integers Nilpotent groups p-adic groups Pro-p-Gruppe (DE-588)4275211-5 gnd rswk-swf Pro-p-Gruppe (DE-588)4275211-5 s DE-604 Du Sautoy, Marcus 1965- Verfasser (DE-588)122205731 aut Mann, Avinoam 1937- Verfasser (DE-588)173586686 aut Segal, Daniel 1947- Verfasser (DE-588)133203670 aut Erscheint auch als Druck-Ausgabe 978-0-521-65011-3 Erscheint auch als Druck-Ausgabe 978-0-521-54218-0 Cambridge studies in advanced mathematics 61 (DE-604)BV044781283 61 https://doi.org/10.1017/CBO9780511470882 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Dixon, John D. 1937- Du Sautoy, Marcus 1965- Mann, Avinoam 1937- Segal, Daniel 1947- Analytic pro-p groups Cambridge studies in advanced mathematics Pt. I. Pro-p groups -- 1. Profinite groups and pro-p groups -- 2. Powerful p-groups -- 3. Pro-p groups of finite rank -- 4. Uniformly powerful groups -- 5. Automorphism groups -- Interlude A. 'Fascicule de resultats': pro-p groups of finite rank -- Pt. II. Analytic groups -- 6. Normed algebras -- 7. The group algebra -- Interlude B. Linearity criteria -- 8. p-adic analytic groups -- Interlude C. Finitely generated groups, p-adic analytic groups and Poincare series -- 9. Lie theory -- Pt. III. Further topics -- 10. Pro-p groups of finite coclass -- 11. Dimension subgroup methods -- 12. Some graded algebras -- Interlude D. The Golod-Shafarevich inequality -- Interlude E. Groups of sub-exponential growth -- 13. Analytic groups over pro-p rings -- App. A. The Hall-Petrescu formula -- App. B. Topological groups Nilpotent groups p-adic groups Pro-p-Gruppe (DE-588)4275211-5 gnd |
| subject_GND | (DE-588)4275211-5 |
| title | Analytic pro-p groups |
| title_auth | Analytic pro-p groups |
| title_exact_search | Analytic pro-p groups |
| title_full | Analytic pro-p groups J.D. Dixon, Carleton University, Ottawa, M.P.F. du Sautoy, University of Cambridge, A. Mann, Hebrew University, Jerusalem, D. Segal, All Souls College Oxford; Revised and enlarged by Marcus du Sautoy & Dan Segal |
| title_fullStr | Analytic pro-p groups J.D. Dixon, Carleton University, Ottawa, M.P.F. du Sautoy, University of Cambridge, A. Mann, Hebrew University, Jerusalem, D. Segal, All Souls College Oxford; Revised and enlarged by Marcus du Sautoy & Dan Segal |
| title_full_unstemmed | Analytic pro-p groups J.D. Dixon, Carleton University, Ottawa, M.P.F. du Sautoy, University of Cambridge, A. Mann, Hebrew University, Jerusalem, D. Segal, All Souls College Oxford; Revised and enlarged by Marcus du Sautoy & Dan Segal |
| title_short | Analytic pro-p groups |
| title_sort | analytic pro p groups |
| topic | Nilpotent groups p-adic groups Pro-p-Gruppe (DE-588)4275211-5 gnd |
| topic_facet | Nilpotent groups p-adic groups Pro-p-Gruppe |
| url | https://doi.org/10.1017/CBO9780511470882 |
| volume_link | (DE-604)BV044781283 |
| work_keys_str_mv | AT dixonjohnd analyticpropgroups AT dusautoymarcus analyticpropgroups AT mannavinoam analyticpropgroups AT segaldaniel analyticpropgroups |